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Validation of Remote Sensing Ocean Wave Data

373

PRESENTATION AND VALIDATION OF REMOTE SENSING OCEAN
WAVE DATA

Omar Yaakob, Norazimar Zainudin, Yahya Samian, Adi Maimun, Abdul Malik & Robiahtul Adawiah Palaraman

Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia, 81310 Skudai, Malaysia

ABSTRACT

The use of satellite wave altimetry has increased the possibility of getting better temporal and spatial coverage of
wave data collection. Whilst the method to obtain wave heights is well established, such is not the case with
methods of derivations of wave periods. This study presents a review of four available methods to derive wave
periods and describes the implementation of such methods to obtain Malaysian ocean waves joint probabilities of
wave heights and wave periods data from TOPEX/Poseidon satellite altimetry. Data is presented in formats similar
to the commonly used Global Wave Statistics. Comparisons are made with measured data from a petroleum
company offshore platform. Results indicate that two methods produced almost identical wave periods data to the
measured data.

Keywords: Aerospace application, Oceanographic data, Satellite Altimetry

1. INTRODUCTION

Satellite altimetry is beginning to be accepted as a reliable method to obtain ocean wave data. Methods to derive
wave data from satellite altimetry have been presented in previous studies, for example by Sakuno [1]. The overall
accuracy of altimeter measurements of Significant Wave Heights (SWH) has been investigated by numerous
comparisons with buoy observations. On average, the T/P estimates were found by Fu and Cazenave [2] to be
smaller than the buoy estimates by about 5% ,
The probability of occurrence of significant wave heights is normally enough for most engineering design
calculations. However, in some cases such as the use of sea spectra to estimate downtime of floating vessels, wave
periods data is required. The most common source for this data is Global Wave Statistics (GWS) data published
by British Maritime Technology, BMT [3]. For example, Table 1 shows GWS joint probability distribution of
wave heights and periods for Area 62 that covers the whole of South China Sea and Gulf of Siam. The accuracy,
reliability and comprehensiveness of such data have often been questioned, for example in Shinkai and Wan [4].
There is thus a need to find wave periods data from satellite altimetry. Although methods to obtain wave heights
probabilities from satellite data are quite well established, this is not the case with wave periods. This study presents
a survey of a number of methods to derived wave periods from various parameters and compares the results of their
implementation for Malaysian sea.

2. MATERIALS AND METHODS

2.1 Wave periods derivation

The derivation of wave periods from altimeter data is still in its early development [5], [6]. There are a number of
methods being developed by researchers in this area. Besides the method by Shinkai and Wan [4], other methods to
derived wave periods are by Davies et al.[6]; Hwang et al. [7] and Gommengiger et al [8].








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Table 1: GWS Joint probability distribution for Area 62 [3]

ALL DIRECTIONS
PERCENTAGE OF OBS = 100.00%
(INCLUDING 2.19% DIRECTION UNKNOWN)
TOTAL 84 284 339 197 72 19 4 1 - - - 1000
>14 - - - - - - - - - - - -
S
I
G
N
I
F
I
C
A
N
T

W
A
V
E

H
E
I
G
H
T


13-14 - - - - - - - - - - - -
12-13 - - - - - - - - - - - -
11-12 - - - - - - - - - - - -
10-11 - - - - - - - - - - - -
9-10 - - - - - - - - - - - -
8-9 - - - - - - - - - - - -
7-8 - - - - - - - - - - - -
6-7 - - 1 1 1 - - - - - - 3
5-6 - 1 2 2 2 1 - - - - - 7
4-5 - 2 6 6 4 2 1 - - - - 20
3-4 1 7 19 19 10 3 1 - - - - 60
2-3 3 30 62 49 21 6 1 - - - - 172
1-2 17 103 146 84 27 6 1 - - - - 385
0-1 63 142 104 36 8 1 - - - - 354
4-5 6-7 8-9 10-11 12-13 TOTAL
<4 5-6 7-8 9-10 11-12 >13
ZERO CROSSING PERIOD (s)


In Shinkai and Wan [4], the period data are obtained by using a general relationship derived from instrumentally
measured data. To obtain this relationship, a joint lognormal probability distribution is fitted to each set of SWH
data. This distribution is given by:

2
T 2
1 (lnT (H))
P(T H) f exp
2 (H) T 2 (H)
(
= =
(
o to

(1)

where, the parameters (H) and o
2
(H) of the fitting procedures are determined from its standard scatter diagram data
by:


| |
| |
(H) E lnT (H)
(H) Var lnT (H)
=

o =

(2)

However, the (H) and o
2
(H) could not get from scatter diagram because of little data when the SWH is greater than
7 m. In this case, they are derived approximately from:


1
1 2
(H) a a lnH
(H) b expb H
= +
o =
(3)

where, H is significant wave height. The parameters a, a
1,
b
1
and b
2
are specific constants are determined from its
standard diagram data by using both the least squared method and extrapolation.

Hwang et al. (1997) has developed the empirical relationship between peak period of the wave field, T, to wind
speed, U and wave height, H and is given by:


2 0.67
U/ (gT) 0.048(U / (gH)) = (4)

where, g is the gravitational constant. Hwang reported that using the T/P data to derive U and H, the period
calculated from (4) was found to be slightly less (by 6%) than the buoy measured peak period.

Davies et al.[6], relating the sigma0 value with the probability distribution of the sea surface slopes allows the
variance of the slopes to be expressed in terms of the spatial spectral moments. Using the dispersion relationship
these can easily be converted into the temporal spectral moments. As a result we can obtain an estimate of the fourth
IJRRAS 4 (4) September 2010 Yaakob & al. Validation of Remote Sensing Ocean Wave Data


375

spectral moment, m4, as a function of sigma0. Combining this with m0, obtained from the significant wave height
value, allows the altimeter to estimate wave period, Ta. So, by analogy an altimeter wave period as equal to:


1/ 4
m0
Ta
m4
| |
=
|
\ .
(5)

Gommengiger et al. [8] produced method that uses the radar backscatter coefficient that is related under the
Geometrical Optics approximation to the inverse of the inverse of the mean square slope (mss) of the long ocean
waves:


0
1
~
mms
o (6)

In turn, ocean wave slope is dimensionally equivalent to the ratio of some measure of the ocean wave height and the
ocean wavelength, L:


SWH
slope ~
L
(7)
The ocean wavelength is related to wave period, T and phase velocity, c, through L = cT.

Under the deep water approximation, the wave phase velocity is related to the ocean wave period through the
dispersion relationship for gravity waves:


gT
c
2
=
t
(8)
so that

2
L ~ T and
2
4
SWH
mss ~
T
(9)
and thus:


0 2 0.25
T ~ ( SWH ) o (10)

2.2 Application to Malaysian sea

The above methods to derive probability of occurrence of wave heights and joint probability distribution of wave
heights and periods are applied to a particular Malaysian sea area. Wave heights data are compared with data from
publications by MMS [9].

3. RESULTS
Results of application of the methods are described for a sea area close to Sarawak Coast. The area selected is in
the South China Sea between the longitude of 112-114E and latitude 4-6. This area was chosen because of the
availability of data in MMS for easier comparison. The data extracted were based on repeat cycle of the T/P satellite
within this area from 1999-2001. Each data file contains text data for 8 hours cycle giving various information
including date and time, locations (latitude and longitude in micro degrees), significant wave height (0.1m) and sea
surface height (mm).

3.2 Comparisons with MMS data

Comparison between quarterly T/P data and MMS data is given in Table 2 for each individual year as well as for the
3-year average. The 3-year averages are also plotted in Fig. 1. It needs to be noted that the comparisons shown are
between averages from altimetry measurements and visual observations, which are in themselves not very accurate.
Nevertheless, the results indicate that significant wave heights from T/P generally agree well with those from MMS.
There is a larger variation in the
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376


Table 2: Comparison of average of significant wave height between MMS and Topex/Poseidon quarterly for 1999-2001
1999 2000 2001 3-Year average
--------------- ------------- ------------- --------------------
MMS T/P MMST/P MMS T/P MMS T/P
Q01 1.1 1.1 1.0 1.0 0.9 0.8 1.000 0.967
Q02 0.6 0.6 0.7 0.7 0.7 0.8 0.667 0.700
Q03 0.8 0.6 0.8 0.7 0.8 0.7 0.800 0.667
Q04 1.2 1.0 0.9 1.4 0.8 1.2 0.967 1.200


Fig. 1: Comparison of 3-year quarterly average of significant wave height between MMS and Topex/Poseidon

fourth quarter average. The difference could be attributed to the fact that there are fewer reports from ships during
the monsoon seasons. For example in 2002, there are nearly one hundred ship reports in the month of July
compared to only about 30 in the month of December. Moreover, the reports that come in are from masters of ships,
which are in the open sea, most of whom will try to avoid heavy seas. Thus the observations from ships can be
expected to be lower compared to the readings from T/P.

3.3 Comparison with GWS data

The annual probability distributions of one-metre classes of wave heights are obtained from T/P data in the period
1999-2001. The final distribution and comparison to GWS data is given in Table 3.The probability of exceedance
curve for each distribution is plotted in Fig. 2. A 3-parameter Weibull function with the following equation are used
to describe the distributions [10].


1
Hs Hs
P(x Hs) exp
| |
( | ( | |
> =
| ( (
o o o
\ .
(11)

where, o, | and are the parameters defining the shape of the curve. By curve fitting methods, the parameters
describing the GWS and T/P distributions for this particular location are obtained and given in Table 4.
Table 3: Comparison of probability occurrence of significant wave height between GWS and TOPEX/poseidon for 1999-2001
P (H) GWS P (H) T/P
0-1 354 637
1-2 385 319
2-3 172 32
3-4 60 11
4-5 20 0
5-6 7 0
6-7 3 0
7-8 1 0
8-9 1 0
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377



Fig. 2:Probability distribution of wave height exceedance


Table 4: Weibull parameters for wave height exceedance cumulative probabilities

Parameter o |
GWS 1.1 1.6 0.2
T/P 0.5 1.0 0.2

.
4. DISCUSSION

The results indicate that the data provided by T/P at the 22 grid is markedly different from that given by GWS
Area 62. It should be noted that GWS gives wave height probability distribution for a large area covering Gulf of
Siam and most of China Sea. As such, wave heights above 4 m are considered probable whilst in the selected
location; such wave heights are never expected to occur. The shape of the probability exceedance curve shows that
generally wave heights are lower at the selected area. Thus designing ocean structures in the selected area using
GWS could lead to erroneous results, at best over design.

4.1 Comparison joint probabilities of wave heights and periods

The same altimetry data is used as input into Shinkai and Wan [4], Hwang et al. [7] and Gommengiger et al. [8]
methods. Each method produces joint probability distributions of wave heights and periods and can be presented in
a similar format to that of GWS. Results from Davis method are not available at the time of writing this study.
Table 5 shows a typical scatter diagram obtained using Hwang et al. [7] method.
Comparison of marginal probability occurrence of wave periods obtained from GWS, Shinkai and Wan method,
Hwang et al. [7] method and Gommengiger et al. [8] method are given in Table 6. The data is plotted in Fig. 3.
It is shown that all methods show similar tends to that of GWS, giving most likely periods to be around 3-5 sec.
There is a close agreement between results from Shinkai and Wan [4] and Gommengiger et al. [8] surprising
because both use different concepts. Are significantly differences among these data. However, all the results from
GWS and Shinkai and Wan method show a good agreement, but probability occurrence of wave period using the
Hwangs results show a double hump which for now could not be characterised. There is a great need to carry out
the validation purposes of this method.








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Table 5: T/P Joint annual probability distribution for 1999-2001 using Hwang et al. [7]

TOTAL 46 160 233 162 207 85 46 37 9 7 7 1000
>14 - - - - - - - - - - - -
S
I
G
N
I
F
I
C
A
N
T

W
A
V
E

H
E
I
G
H
T


(
c
m
)

13-14 - - - - - - - - - - - -
12-13 - - - - - - - - - - - -
11-12 - - - - - - - - - - - -
10-11 - - - - - - - - - - - -
9-10 - - - - - - - - - - - -
8-9 - - - - - - - - - - - -
7-8 - - - - - - - - - - - -
6-7 - - - - - - - - - - - -
5-6 - - - - - - - - - - - -
4-5 - - - - - - - - - - - -
3-4 - - - - - 1 3 7 - - - 9
2-3 - - - - 8 20 4 - - - - 32
1-2 - - 5 74 151 38 18 14 5 7 7 319
0-1 46 160 228 88 48 27 21 16 4 - - 637
3-4 5-6 7-8 9-10 11-12 TOTAL
<3 4-5 6-7 8-9 10-11 >12
ZERO CROSSING PERIOD (s)

Table 6: Comparison of marginal probability of occurrence of wave period using GWS data, Shinkai and Wan
method and Hwang et al method
Shinkai and Wan Hwang et al. Gommengiger
GWS (1996) (1997) et al. (2003)
<3 84 156 46 141
3-4 284 254 160 239
4-5 339 238 233 241
5-6 197 168 162 135
6-7 72 101 207 111
7-8 19 55 85 75
8-9 4 29 46 35
9-10 1 0 37 9
10-11 0 0 9 3
11-12 0 0 7 2
>12 0 0 8 10


Fig. 3: Probability distribution of wave height exceedance
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5. CONCLUSION

It has been shown that more comprehensive data can be obtained for all sea areas using satellite altimetry data.
Comparison with presently available data based on visual observation has shown encouraging results. The data
provided by TOPEX/Poseidon satellite can be used to derive wave periods, which can then be used to obtain joint
probability distribution of wave heights and periods. Four methods to derive wave periods have been described and
their implementation on a particular Malaysian sea area has been presented. The results indicate that the methods
produces similar trends. However there is a need to obtain in-situ measurement for validation of these results.

6. ACKNOWLEDGEMENT

The researcher wish to thank National MOSTI who supported the project under the IRPA programme. Special
thanks are due Division of Marine Meteorology and Oceanography, Malaysian Meteorological Service for their
support and assistance. The authors also wish to thank Dr. Yuji Sakuno from Hiroshima University for his help and
advice in this project.

7. REFERENCES

[1] Sakuno, Y., Iijima, y., Preliminary study for a method of long term wave data collection and GIS construction
in Indonesian domestic sea using satellite data. Proceedings of the Japanese Conference on Remote Sensing,
Journal Code:X0715A Vol.33; pp.285-286, 2002.
[2] Fu, L.L. and A. Cazenave, Satellite Altimetry and Earth Sciences: A Handbook of Techniques and Application.
Academic Press, London. 1st edition, ISBN: 0122695453 2001.
[3] British Maritime Technology Ltd, Global Wave Statistic. Unwin, London, ISBN: 0946653380 1986.
[4] Shinkai A. and S. Wan, Statistical characteritics of Global Wave data and the appraisal for long-term predictions
of ship response, Journal of the Society of Naval Architects of Japan ISSN 0514-8499
1995, vol. 178, pp. 289-296.
[5] Carter, D.J.T., P.G. Challenor and M.A. Srokosz,, An assessment of GEOSAT wave height and wind speed
measurements,1992 J. Geophys. Res., 97: 11383-11392.
[6] Davies, C.G., G.C. Peter and P.D. Cotton, Measurements of wave period from radar altimeters. Proceeding of the
International Symposium on Ocean Wave Measurement and Analysis, September 2-6, 2001, San Francisco,
CA, pp: 819-826.
[7] Hwang, P.A., W.J. Teague, D.W.C. Wang, E.F. Thompson and G.A. Jacobs, A wave/wind climatology
for the gulf of Mexico. Proceedings of the Seventh International. Offshore and Polar Engineering Conference.
Honolulu, Hawaii, USA, May 25-30, 1997.
[8] Gommengiger, C.P., M.A. Srokosz, P.G. Challenor and P.D. Cotton, An empirical model to retrieving ocean
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Symposium - IGARSS 2003, Toulouse (France) 21-25 July 2003, pp: 2706-2708.
[9] Malaysian Meteorological Department Monthly Summary of Marine Meteorological Observation, 1999, 2000,
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[10] Omar Yaakob, Norazimar Zainuddin, Preliminary Work In Using Satellite Wave Data To Develop Malaysian
Ocean Wave Database, Journal of Physical Science, ISSN: 1675-3402, Vol. 16(2), pp. 135-143, 2005.